Question: Simplify; express your answer in exponential form. Assume $r\neq 0, n\neq 0$. $\dfrac{{(r^{3}n^{-5})^{3}}}{{(rn^{-3})^{-1}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(r^{3}n^{-5})^{3} = (r^{3})^{3}(n^{-5})^{3}}$ On the left, we have ${r^{3}}$ to the exponent ${3}$ . Now ${3 \times 3 = 9}$ , so ${(r^{3})^{3} = r^{9}}$ Apply the ideas above to simplify the equation. $\dfrac{{(r^{3}n^{-5})^{3}}}{{(rn^{-3})^{-1}}} = \dfrac{{r^{9}n^{-15}}}{{r^{-1}n^{3}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{9}n^{-15}}}{{r^{-1}n^{3}}} = \dfrac{{r^{9}}}{{r^{-1}}} \cdot \dfrac{{n^{-15}}}{{n^{3}}} = r^{{9} - {(-1)}} \cdot n^{{-15} - {3}} = r^{10}n^{-18}$